<p>Recent ecological studies have focused on mathematical modeling, analysis and simulations of the spatial-temporal population distribution of interacting species. In this work, we try to comprehend the spatiotemporal dynamics that are impacted by the prey-taxis coefficient in an environment where generalist predators induce fear and have carryover effects that trigger both prey and predator populations to form clusters. By validating the analytical requirements, the suggested model exhibits a finite-time blow-up dependent on initial data. This phenomenon has been numerically confirmed for predator species. In addition, we expand the spatial model in a discrete environment. Stability analysis has been done for the non-spatial model, the spatial model on networks, and the continuous medium. This study explores the development of spatial patterns in both networked and non-networked environments, specifically comparing the formation of Turing patterns in network framework with those observed in continuous media while considering various network topologies. The combined effects of the fear parameter, network structures, and the prey-taxis coefficient are shown to influence Turing patterns. Different parameter sets cause distinctive patterns, like spots and stripes, to emerge gradually. Our simulations demonstrate the effects of various network layouts, namely Lattice (LA), Barabási-Albert (BA), and Watts-Strogatz (WS) networks, on the node density distribution and the time needed for patterns to stabilize. We also show how the internal dynamics of networks influence species distribution in their environments. These discoveries offer crucial new understandings of the intricate dynamics of prey-predator interactions in ecological networks.</p>